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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math.analysis.integration;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math.FunctionEvaluationException;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math.MathRuntimeException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math.MaxIterationsExceededException;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math.analysis.UnivariateRealFunction;<a name="line.22"></a>
<FONT color="green">023</FONT>    <a name="line.23"></a>
<FONT color="green">024</FONT>    /**<a name="line.24"></a>
<FONT color="green">025</FONT>     * Implements the &lt;a href="http://mathworld.wolfram.com/TrapezoidalRule.html"&gt;<a name="line.25"></a>
<FONT color="green">026</FONT>     * Trapezoidal Rule&lt;/a&gt; for integration of real univariate functions. For<a name="line.26"></a>
<FONT color="green">027</FONT>     * reference, see &lt;b&gt;Introduction to Numerical Analysis&lt;/b&gt;, ISBN 038795452X,<a name="line.27"></a>
<FONT color="green">028</FONT>     * chapter 3.<a name="line.28"></a>
<FONT color="green">029</FONT>     * &lt;p&gt;<a name="line.29"></a>
<FONT color="green">030</FONT>     * The function should be integrable.&lt;/p&gt;<a name="line.30"></a>
<FONT color="green">031</FONT>     *  <a name="line.31"></a>
<FONT color="green">032</FONT>     * @version $Revision: 799857 $ $Date: 2009-08-01 09:07:12 -0400 (Sat, 01 Aug 2009) $<a name="line.32"></a>
<FONT color="green">033</FONT>     * @since 1.2<a name="line.33"></a>
<FONT color="green">034</FONT>     */<a name="line.34"></a>
<FONT color="green">035</FONT>    public class TrapezoidIntegrator extends UnivariateRealIntegratorImpl {<a name="line.35"></a>
<FONT color="green">036</FONT>    <a name="line.36"></a>
<FONT color="green">037</FONT>        /** Intermediate result. */<a name="line.37"></a>
<FONT color="green">038</FONT>        private double s;<a name="line.38"></a>
<FONT color="green">039</FONT>    <a name="line.39"></a>
<FONT color="green">040</FONT>        /**<a name="line.40"></a>
<FONT color="green">041</FONT>         * Construct an integrator for the given function.<a name="line.41"></a>
<FONT color="green">042</FONT>         * <a name="line.42"></a>
<FONT color="green">043</FONT>         * @param f function to integrate<a name="line.43"></a>
<FONT color="green">044</FONT>         * @deprecated as of 2.0 the integrand function is passed as an argument<a name="line.44"></a>
<FONT color="green">045</FONT>         * to the {@link #integrate(UnivariateRealFunction, double, double)}method.<a name="line.45"></a>
<FONT color="green">046</FONT>         */<a name="line.46"></a>
<FONT color="green">047</FONT>        @Deprecated<a name="line.47"></a>
<FONT color="green">048</FONT>        public TrapezoidIntegrator(UnivariateRealFunction f) {<a name="line.48"></a>
<FONT color="green">049</FONT>            super(f, 64);<a name="line.49"></a>
<FONT color="green">050</FONT>        }<a name="line.50"></a>
<FONT color="green">051</FONT>    <a name="line.51"></a>
<FONT color="green">052</FONT>        /**<a name="line.52"></a>
<FONT color="green">053</FONT>         * Construct an integrator.<a name="line.53"></a>
<FONT color="green">054</FONT>         */<a name="line.54"></a>
<FONT color="green">055</FONT>        public TrapezoidIntegrator() {<a name="line.55"></a>
<FONT color="green">056</FONT>            super(64);<a name="line.56"></a>
<FONT color="green">057</FONT>        }<a name="line.57"></a>
<FONT color="green">058</FONT>    <a name="line.58"></a>
<FONT color="green">059</FONT>        /**<a name="line.59"></a>
<FONT color="green">060</FONT>         * Compute the n-th stage integral of trapezoid rule. This function<a name="line.60"></a>
<FONT color="green">061</FONT>         * should only be called by API &lt;code&gt;integrate()&lt;/code&gt; in the package.<a name="line.61"></a>
<FONT color="green">062</FONT>         * To save time it does not verify arguments - caller does.<a name="line.62"></a>
<FONT color="green">063</FONT>         * &lt;p&gt;<a name="line.63"></a>
<FONT color="green">064</FONT>         * The interval is divided equally into 2^n sections rather than an<a name="line.64"></a>
<FONT color="green">065</FONT>         * arbitrary m sections because this configuration can best utilize the<a name="line.65"></a>
<FONT color="green">066</FONT>         * alrealy computed values.&lt;/p&gt;<a name="line.66"></a>
<FONT color="green">067</FONT>         *<a name="line.67"></a>
<FONT color="green">068</FONT>         * @param f the integrand function<a name="line.68"></a>
<FONT color="green">069</FONT>         * @param min the lower bound for the interval<a name="line.69"></a>
<FONT color="green">070</FONT>         * @param max the upper bound for the interval<a name="line.70"></a>
<FONT color="green">071</FONT>         * @param n the stage of 1/2 refinement, n = 0 is no refinement<a name="line.71"></a>
<FONT color="green">072</FONT>         * @return the value of n-th stage integral<a name="line.72"></a>
<FONT color="green">073</FONT>         * @throws FunctionEvaluationException if an error occurs evaluating the<a name="line.73"></a>
<FONT color="green">074</FONT>         * function<a name="line.74"></a>
<FONT color="green">075</FONT>         */<a name="line.75"></a>
<FONT color="green">076</FONT>        double stage(final UnivariateRealFunction f,<a name="line.76"></a>
<FONT color="green">077</FONT>                     final double min, final double max, final int n)<a name="line.77"></a>
<FONT color="green">078</FONT>            throws FunctionEvaluationException {<a name="line.78"></a>
<FONT color="green">079</FONT>            <a name="line.79"></a>
<FONT color="green">080</FONT>            long i, np;<a name="line.80"></a>
<FONT color="green">081</FONT>            double x, spacing, sum = 0;<a name="line.81"></a>
<FONT color="green">082</FONT>            <a name="line.82"></a>
<FONT color="green">083</FONT>            if (n == 0) {<a name="line.83"></a>
<FONT color="green">084</FONT>                s = 0.5 * (max - min) * (f.value(min) + f.value(max));<a name="line.84"></a>
<FONT color="green">085</FONT>                return s;<a name="line.85"></a>
<FONT color="green">086</FONT>            } else {<a name="line.86"></a>
<FONT color="green">087</FONT>                np = 1L &lt;&lt; (n-1);           // number of new points in this stage<a name="line.87"></a>
<FONT color="green">088</FONT>                spacing = (max - min) / np; // spacing between adjacent new points<a name="line.88"></a>
<FONT color="green">089</FONT>                x = min + 0.5 * spacing;    // the first new point<a name="line.89"></a>
<FONT color="green">090</FONT>                for (i = 0; i &lt; np; i++) {<a name="line.90"></a>
<FONT color="green">091</FONT>                    sum += f.value(x);<a name="line.91"></a>
<FONT color="green">092</FONT>                    x += spacing;<a name="line.92"></a>
<FONT color="green">093</FONT>                }<a name="line.93"></a>
<FONT color="green">094</FONT>                // add the new sum to previously calculated result<a name="line.94"></a>
<FONT color="green">095</FONT>                s = 0.5 * (s + sum * spacing);<a name="line.95"></a>
<FONT color="green">096</FONT>                return s;<a name="line.96"></a>
<FONT color="green">097</FONT>            }<a name="line.97"></a>
<FONT color="green">098</FONT>        }<a name="line.98"></a>
<FONT color="green">099</FONT>    <a name="line.99"></a>
<FONT color="green">100</FONT>        /** {@inheritDoc} */<a name="line.100"></a>
<FONT color="green">101</FONT>        @Deprecated<a name="line.101"></a>
<FONT color="green">102</FONT>        public double integrate(final double min, final double max)<a name="line.102"></a>
<FONT color="green">103</FONT>            throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {<a name="line.103"></a>
<FONT color="green">104</FONT>            return integrate(f, min, max);<a name="line.104"></a>
<FONT color="green">105</FONT>        }<a name="line.105"></a>
<FONT color="green">106</FONT>    <a name="line.106"></a>
<FONT color="green">107</FONT>        /** {@inheritDoc} */<a name="line.107"></a>
<FONT color="green">108</FONT>        public double integrate(final UnivariateRealFunction f,<a name="line.108"></a>
<FONT color="green">109</FONT>                                final double min, final double max)<a name="line.109"></a>
<FONT color="green">110</FONT>            throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {<a name="line.110"></a>
<FONT color="green">111</FONT>            <a name="line.111"></a>
<FONT color="green">112</FONT>            int i = 1;<a name="line.112"></a>
<FONT color="green">113</FONT>            double t, oldt;<a name="line.113"></a>
<FONT color="green">114</FONT>            <a name="line.114"></a>
<FONT color="green">115</FONT>            clearResult();<a name="line.115"></a>
<FONT color="green">116</FONT>            verifyInterval(min, max);<a name="line.116"></a>
<FONT color="green">117</FONT>            verifyIterationCount();<a name="line.117"></a>
<FONT color="green">118</FONT>    <a name="line.118"></a>
<FONT color="green">119</FONT>            oldt = stage(f, min, max, 0);<a name="line.119"></a>
<FONT color="green">120</FONT>            while (i &lt;= maximalIterationCount) {<a name="line.120"></a>
<FONT color="green">121</FONT>                t = stage(f, min, max, i);<a name="line.121"></a>
<FONT color="green">122</FONT>                if (i &gt;= minimalIterationCount) {<a name="line.122"></a>
<FONT color="green">123</FONT>                    final double delta = Math.abs(t - oldt);<a name="line.123"></a>
<FONT color="green">124</FONT>                    final double rLimit =<a name="line.124"></a>
<FONT color="green">125</FONT>                        relativeAccuracy * (Math.abs(oldt) + Math.abs(t)) * 0.5; <a name="line.125"></a>
<FONT color="green">126</FONT>                    if ((delta &lt;= rLimit) || (delta &lt;= absoluteAccuracy)) {<a name="line.126"></a>
<FONT color="green">127</FONT>                        setResult(t, i);<a name="line.127"></a>
<FONT color="green">128</FONT>                        return result;<a name="line.128"></a>
<FONT color="green">129</FONT>                    }<a name="line.129"></a>
<FONT color="green">130</FONT>                }<a name="line.130"></a>
<FONT color="green">131</FONT>                oldt = t;<a name="line.131"></a>
<FONT color="green">132</FONT>                i++;<a name="line.132"></a>
<FONT color="green">133</FONT>            }<a name="line.133"></a>
<FONT color="green">134</FONT>            throw new MaxIterationsExceededException(maximalIterationCount);<a name="line.134"></a>
<FONT color="green">135</FONT>        }<a name="line.135"></a>
<FONT color="green">136</FONT>    <a name="line.136"></a>
<FONT color="green">137</FONT>        /** {@inheritDoc} */<a name="line.137"></a>
<FONT color="green">138</FONT>        @Override<a name="line.138"></a>
<FONT color="green">139</FONT>        protected void verifyIterationCount() throws IllegalArgumentException {<a name="line.139"></a>
<FONT color="green">140</FONT>            super.verifyIterationCount();<a name="line.140"></a>
<FONT color="green">141</FONT>            // at most 64 bisection refinements<a name="line.141"></a>
<FONT color="green">142</FONT>            if (maximalIterationCount &gt; 64) {<a name="line.142"></a>
<FONT color="green">143</FONT>                throw MathRuntimeException.createIllegalArgumentException(<a name="line.143"></a>
<FONT color="green">144</FONT>                        "invalid iteration limits: min={0}, max={1}",<a name="line.144"></a>
<FONT color="green">145</FONT>                        0, 64);<a name="line.145"></a>
<FONT color="green">146</FONT>            }<a name="line.146"></a>
<FONT color="green">147</FONT>        }<a name="line.147"></a>
<FONT color="green">148</FONT>    }<a name="line.148"></a>




























































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